Question Number 62570 by aliesam last updated on 23/Jun/19 Commented by mathmax by abdo last updated on 23/Jun/19 $${we}\:{have}\:{S}\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{sin}\left({nx}\right)}{\mathrm{2}^{{n}−\mathrm{1}} }\:=\mathrm{2}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{sin}\left({nx}\right)}{\mathrm{2}^{{n}} }\:=\mathrm{2}\:{Im}\left(\sum_{{n}=\mathrm{1}}…
Question Number 128105 by snipers237 last updated on 04/Jan/21 $${Let}\:{f}\:\:\:\mathbb{N}^{\ast} \rightarrow\mathbb{N}^{\ast} \:{a}\:{bijection}\: \\ $$$${Prove}\:{that}\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left({k}\right)\geqslant\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128103 by byaw last updated on 04/Jan/21 $$ \\ $$$$\mathrm{A}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{4}\:\mathrm{black}\:\mathrm{5}\:\mathrm{white} \\ $$$$\mathrm{and}\:\mathrm{6}\:\mathrm{red}\:\mathrm{shirts}.\:\mathrm{3}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{box}\:\mathrm{one}\:\mathrm{after}\:\mathrm{the}\:\mathrm{other}\: \\ $$$$\mathrm{without}\:\mathrm{replacement}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{proability}\:\mathrm{that}\:\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{color}\:\mathrm{and}\:\mathrm{one}\:\mathrm{a}\:\mathrm{different}\:\mathrm{color}. \\ $$ Answered…
Question Number 128094 by TITA last updated on 04/Jan/21 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\:\mathrm{in}\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{2}\pi \\ $$$$\mathrm{sin}\:\mathrm{2x}=\mathrm{sec}\:\mathrm{x} \\ $$ Answered by MJS_new last updated on 04/Jan/21 $$\mathrm{sin}\:\mathrm{2}{x}\:=\mathrm{2sin}\:{x}\:\mathrm{cos}\:{x} \\ $$$$\mathrm{sin}\:{x}\:={s} \\…
Question Number 128093 by BHOOPENDRA last updated on 04/Jan/21 Answered by Dwaipayan Shikari last updated on 04/Jan/21 $$\mathscr{L}\left({e}^{\mathrm{2}{t}} +\mathrm{4}{t}^{\mathrm{3}} −\mathrm{2}{sin}\mathrm{3}{t}+\mathrm{3}{cos}\mathrm{3}{t}\right) \\ $$$$=\int_{\mathrm{0}} ^{\infty} {e}^{\mathrm{2}{t}−{st}} +\int_{\mathrm{0}}…
Question Number 62556 by naka3546 last updated on 22/Jun/19 $$\frac{\mathrm{1}+\mathrm{3}}{\mathrm{3}}\:+\:\frac{\mathrm{1}+\mathrm{3}+\mathrm{5}}{\mathrm{3}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}}{\mathrm{3}^{\mathrm{3}} }\:+\:…\:\:=\:\:\:\frac{{a}}{{b}}\:\:,\:\:{a},\:{b}\:\in\:\:\mathbb{Z}^{+} \: \\ $$ Commented by Prithwish sen last updated on 22/Jun/19 $$\mathrm{t}_{\mathrm{n}} =\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}}…
Question Number 128090 by ajfour last updated on 04/Jan/21 $${someone}\:{help}\:{cheking}\:{this}: \\ $$$$\:\:\:\:{x}^{\mathrm{3}} ={x}+{c}\:\: \\ $$$${let}\:\:{x}=\left({p}−\mathrm{2}{q}\right)+\left({q}−\mathrm{2}{p}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:=\:−\left({p}+{q}\right) \\ $$$${p}^{\mathrm{3}} −\mathrm{8}{q}^{\mathrm{3}} −\mathrm{6}{pq}\left({p}−\mathrm{2}{q}\right)+ \\ $$$${q}^{\mathrm{3}} −\mathrm{8}{p}^{\mathrm{3}} −\mathrm{6}{pq}\left({q}−\mathrm{2}{p}\right)+…
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Question Number 62554 by Rasheed.Sindhi last updated on 22/Jun/19 $${If}\:{a}\:\&\:{b}\:{are}\:{two}\:{natural}\:{numbers} \\ $$$${then}\:{the}\:{following}\:{relation}\:{holds} \\ $$$${always}. \\ $$$$\:\:\:\:\:{a}×{b}=\mathrm{gcd}\left({a},{b}\right)×\mathrm{lcm}\left({a},{b}\right) \\ $$$$\:^{\bullet} {If}\:{a},{b}\:\&\:{c}\:\:{are}\:{three}\:{natural}\:{numbers} \\ $$$$\:\:\:{what}\:{relation}\left({anologous}\:{to}\:{the}\:{above}\right) \\ $$$$\:\:\:\:{holds}\:{between}\:{numbers}\:{and}\:{their} \\ $$$$\:\:\:\mathrm{gcd}\:\&\:\mathrm{lcm}?…
Question Number 128082 by liberty last updated on 04/Jan/21 $$\beta\:=\:\int\:\frac{\mathrm{1}+\mathrm{ln}\:\left(\mathrm{x}\right)}{\mathrm{x}.\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com